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A244302 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 8. 2
9, 45, 539, 3290, 25234, 156743, 1042823, 6374389, 40710734, 245996972, 1533537330, 9295148728, 57412881670, 349869872571, 2159393201713, 13252915145611, 82161769477646, 508497521855467, 3174435344149894, 19827435510586970, 124802677329672826 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,1

COMMENTS

Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 8.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..90

MAPLE

h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+

    add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end:

g:= proc(n, i, l) local j; `if`(n=0 or i<1, 0, `if`(l<>[] and

      l[1]-i=8, `if`(irem(n, i, 'j')=0, h([l[], i$j]), 0),

      add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i)))

    end:

a:= n-> g(n$2, []):

seq(a(n), n=10..35);

CROSSREFS

Column k=8 of A238707.

Sequence in context: A009432 A145757 A058824 * A177742 A322892 A355175

Adjacent sequences:  A244299 A244300 A244301 * A244303 A244304 A244305

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 25 2014

STATUS

approved

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Last modified August 11 20:13 EDT 2022. Contains 356067 sequences. (Running on oeis4.)